Order of Operations Speed Solving Activity for 3rd-5th Grade - Free Printable

Problem Description:

The image shows a worksheet titled "Order of Operations Speed Challenge." The task is to solve the given mathematical expressions following the PEMDAS rule (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Additionally, the instructions mention recording the time taken to solve the problems and adding 10 seconds for each incorrect response.

Solution Approach:

We will solve each problem step by step, adhering strictly to the PEMDAS order. Let's go through each expression one by one.

---

#### Problem 1: \( 8 + 9 \times 2 = \)
- Step 1: Perform multiplication first (\( 9 \times 2 \)).
\[
9 \times 2 = 18
\]
- Step 2: Add the result to 8.
\[
8 + 18 = 26
\]
- Answer: \( 26 \)

---

#### Problem 2: \( 3 \times 7 + 2 = \)
- Step 1: Perform multiplication first (\( 3 \times 7 \)).
\[
3 \times 7 = 21
\]
- Step 2: Add 2 to the result.
\[
21 + 2 = 23
\]
- Answer: \( 23 \)

---

#### Problem 3: \( 45 - 2 \times 11 = \)
- Step 1: Perform multiplication first (\( 2 \times 11 \)).
\[
2 \times 11 = 22
\]
- Step 2: Subtract the result from 45.
\[
45 - 22 = 23
\]
- Answer: \( 23 \)

---

#### Problem 4: \( 6 + (9 + 9) \div 3 = \)
- Step 1: Solve the parentheses (\( 9 + 9 \)).
\[
9 + 9 = 18
\]
- Step 2: Perform division (\( 18 \div 3 \)).
\[
18 \div 3 = 6
\]
- Step 3: Add the result to 6.
\[
6 + 6 = 12
\]
- Answer: \( 12 \)

---

#### Problem 5: \( 15 - 3 \times 3 = \)
- Step 1: Perform multiplication first (\( 3 \times 3 \)).
\[
3 \times 3 = 9
\]
- Step 2: Subtract the result from 15.
\[
15 - 9 = 6
\]
- Answer: \( 6 \)

---

#### Problem 6: \( 10 - (2 \times 3 + 4) = \)
- Step 1: Solve the parentheses.
- First, perform multiplication (\( 2 \times 3 \)).
\[
2 \times 3 = 6
\]
- Then, add 4.
\[
6 + 4 = 10
\]
- Step 2: Subtract the result from 10.
\[
10 - 10 = 0
\]
- Answer: \( 0 \)

---

#### Problem 7: \( 8 + 6 \times 2 \div 2 = \)
- Step 1: Perform multiplication and division from left to right.
- First, multiply (\( 6 \times 2 \)).
\[
6 \times 2 = 12
\]
- Then, divide (\( 12 \div 2 \)).
\[
12 \div 2 = 6
\]
- Step 2: Add the result to 8.
\[
8 + 6 = 14
\]
- Answer: \( 14 \)

---

#### Problem 8: \( 4 \times 9 \div 0 = \)
- Step 1: Division by zero is undefined.
- Answer: Undefined

---

#### Problem 9: \( 72 \div 8 + 15 = \)
- Step 1: Perform division first (\( 72 \div 8 \)).
\[
72 \div 8 = 9
\]
- Step 2: Add the result to 15.
\[
9 + 15 = 24
\]
- Answer: \( 24 \)

---

#### Problem 10: \( (40 + 8) \div 7 = \)
- Step 1: Solve the parentheses (\( 40 + 8 \)).
\[
40 + 8 = 48
\]
- Step 2: Perform division.
\[
48 \div 7 = 6.857 \, (\text{or } 6 \text{ remainder } 6)
\]
- Answer: \( 6.857 \) (or \( 6 \text{ R } 6 \))

---

#### Problem 11: \( 63 \div (4 + 3) = \)
- Step 1: Solve the parentheses (\( 4 + 3 \)).
\[
4 + 3 = 7
\]
- Step 2: Perform division.
\[
63 \div 7 = 9
\]
- Answer: \( 9 \)

---

#### Problem 12: \( 88 - 14 \div (3 \times 1) = \)
- Step 1: Solve the parentheses (\( 3 \times 1 \)).
\[
3 \times 1 = 3
\]
- Step 2: Perform division (\( 14 \div 3 \)).
\[
14 \div 3 = 4.667 \, (\text{or } 4 \text{ remainder } 2)
\]
- Step 3: Subtract the result from 88.
\[
88 - 4.667 = 83.333 \, (\text{or } 83 \text{ remainder } 2)
\]
- Answer: \( 83.333 \) (or \( 83 \text{ R } 2 \))

---

#### Problem 13: \( 13 + 20 \times 8 \div 7 = \)
- Step 1: Perform multiplication and division from left to right.
- First, multiply (\( 20 \times 8 \)).
\[
20 \times 8 = 160
\]
- Then, divide (\( 160 \div 7 \)).
\[
160 \div 7 = 22.857 \, (\text{or } 22 \text{ remainder } 6)
\]
- Step 2: Add the result to 13.
\[
13 + 22.857 = 35.857 \, (\text{or } 35 \text{ remainder } 6)
\]
- Answer: \( 35.857 \) (or \( 35 \text{ R } 6 \))

---

#### Problem 14: \( (99 - 90) \div 3 = \)
- Step 1: Solve the parentheses (\( 99 - 90 \)).
\[
99 - 90 = 9
\]
- Step 2: Perform division.
\[
9 \div 3 = 3
\]
- Answer: \( 3 \)

---

#### Problem 15: \( 100 - (20 \times 5) = \)
- Step 1: Solve the parentheses (\( 20 \times 5 \)).
\[
20 \times 5 = 100
\]
- Step 2: Subtract the result from 100.
\[
100 - 100 = 0
\]
- Answer: \( 0 \)

---

#### Problem 16: \( 17 + 8 \div 0 = \)
- Step 1: Division by zero is undefined.
- Answer: Undefined

---

#### Problem 17: \( (2 \times 3) - 8 \div 6 = \)
- Step 1: Solve the parentheses (\( 2 \times 3 \)).
\[
2 \times 3 = 6
\]
- Step 2: Perform division (\( 8 \div 6 \)).
\[
8 \div 6 = 1.333 \, (\text{or } 1 \text{ remainder } 2)
\]
- Step 3: Subtract the result from 6.
\[
6 - 1.333 = 4.667 \, (\text{or } 4 \text{ remainder } 2)
\]
- Answer: \( 4.667 \) (or \( 4 \text{ R } 2 \))

---

#### Problem 18: \( 9 \div 3 + (5 + 3) = \)
- Step 1: Solve the parentheses (\( 5 + 3 \)).
\[
5 + 3 = 8
\]
- Step 2: Perform division (\( 9 \div 3 \)).
\[
9 \div 3 = 3
\]
- Step 3: Add the results.
\[
3 + 8 = 11
\]
- Answer: \( 11 \)

---

#### Problem 19: \( 17 \times (4 + 6) = \)
- Step 1: Solve the parentheses (\( 4 + 6 \)).
\[
4 + 6 = 10
\]
- Step 2: Perform multiplication.
\[
17 \times 10 = 170
\]
- Answer: \( 170 \)

---

#### Problem 20: \( 55 - (10 \div 5) = \)
- Step 1: Solve the parentheses (\( 10 \div 5 \)).
\[
10 \div 5 = 2
\]
- Step 2: Subtract the result from 55.
\[
55 - 2 = 53
\]
- Answer: \( 53 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 26 \\
2. & 23 \\
3. & 23 \\
4. & 12 \\
5. & 6 \\
6. & 0 \\
7. & 14 \\
8. & \text{Undefined} \\
9. & 24 \\
10. & 6.857 \, (\text{or } 6 \text{ R } 6) \\
11. & 9 \\
12. & 83.333 \, (\text{or } 83 \text{ R } 2) \\
13. & 35.857 \, (\text{or } 35 \text{ R } 6) \\
14. & 3 \\
15. & 0 \\
16. & \text{Undefined} \\
17. & 4.667 \, (\text{or } 4 \text{ R } 2) \\
18. & 11 \\
19. & 170 \\
20. & 53 \\
\end{array}
}
\]